Robin van Persie's 27th-minute header against his former club settled the match at Old Trafford and lifted United to fifth place. Arsenal lost for the second time this season and its lead over second-place Liverpool was trimmed to two points.
With Man City losing 1-0 at struggling Sunderland and Tottenham beaten at home by Newcastle by the same score, just six points separate Arsenal and eighth-place City after 11 matches in what is proving to be a tight title race.
''What we have learned today is that not only Man United can beat Arsenal but that everybody can beat everybody in this Premier League,'' Arsenal manager Arsene Wenger said.
Phil Bardsley scored the winner in the 21st minute for Sunderland, which started the day even on points with last-place Crystal Palace. City has taken only four points from a possible 18 on the road.
More doubts were raised about Tottenham's top-four credentials. Loic Remy struck a 13th-minute winner at White Hart Lane, with Newcastle goalkeeper Tim Krul preserving the victory with brilliant saves.
''I think Tim Krul was the key to the game,'' Tottenham manager Andre Villas-Boas said. ''He made the difference.''
The Spurs did not play goalkeeper Hugo Lloris, who was knocked unconscious during a match against Everton last weekend. Lloris also missed the midweek Europa League win over Sheriff Tiraspol despite having stayed in the game against Everton.
In Sunday's other match, Charlie Adam converted a penalty kick in the sixth minute of second-half stoppage time to salvage Stoke's 3-3 draw at Swansea.
The draw temporarily left Madrid even at the top of the standings with Barcelona, which can restore its lead at last-place Real Betis later.
Atletico went ahead two minutes into the match when Juanfran Torres broke free on the right flank and swung in a cross that Mario Perez turned into his own net.
Jeremy Perbet tied it when he collected the ball from a throw-in, dribbled into the area and provided a pass that Juanfran ended up poking into his own goal while jostling with Villarreal's Ikechukwu Uche.
Villarreal is in fourth place, but seven points behind Real Madrid in third.
Earlier, Sevilla beat Espanyol 3-1 to end a 22-game winless run away from home in the league. Valencia was held to a 2-2 draw by Valladolid to remain without a victory in its last three home games.
FRANKFURT, Germany (AP) - Eintracht Frankfurt fell to its fourth straight loss in the Bundesliga when Eric Choupo-Moting scored late in the match for Mainz to win 1-0.
Timo Werner, 17, became the youngest player in Bundesliga history to score two goals in a game, leading Stuttgart to a 3-1 victory over Freiburg.
PARIS (AP) - Andre-Pierre Gignac scored a late penalty kick and Marseille defeated struggling Sochaux 2-1 in the French league for its first win in eight games.
Gignac scored in the 83rd minute, sending Marseille to its first win since Sept. 28 after six defeats and one draw.
Marseille, which has lost all four of its matches in the Champions League this season, is in fifth place with 21 points. It is two points behind fourth-place Nantes, which won 3-0 at Bordeaux earlier Sunday.
Paris Saint-Germain remains unbeaten and has a four-point lead over second-place Lille and leads Monaco by five.
MILAN (AP) - Roma was held to a 1-1 draw at home by lowly Sassuolo after yielding a last-minute tying goal. AC Milan's struggles persisted with a 0-0 draw at last-place Chievo Verona in Serie A.
Sassuolo defender Alessandro Longhi's own goal looked to have secured victory for Roma but 19-year-old Domenico Berardi, who scored a hat trick last week, tied it with the last kick of the game.
Roma is four points ahead of Juventus and Napoli, which play each other later Sunday in Turin.
Milan has picked up just two points in four rounds and coach Massimiliano Allegri's job is at risk.
''If the club thinks this team needs another coach at this time then they'll let me know,'' Allegri said.
Lazio drew 1-1 at Parma, while Hellas Verona lost 2-0 at Genoa. A pair of Daniele Conti free kicks helped Cagliari to a 2-1 victory over Torino, ending a run of three successive defeats.
Marko Livaja scored in stoppage time, giving Atalanta a 2-1 victory against Bologna.
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